Urcohomologies and cohomologies of -complexes

  • Naoya Hiramatsu

    Okayama University, Japan
  • Goro C. Kato

    California Polytechnic State University, San Luis Obispo, USA


For a general sequence of objects and morphisms, we construct two -complexes. Then we can define cohomologies -type of the -complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of -complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of -complexes are given.

Cite this article

Naoya Hiramatsu, Goro C. Kato, Urcohomologies and cohomologies of -complexes. Port. Math. 67 (2010), no. 4, pp. 511–524

DOI 10.4171/PM/1875